Conditional probability

Conditional probability is one of the most important concepts in probability theory. In theory it is the probability that a given event occurs given the knowledge of some partial information about the results of the experiment.

For example, take a die tossing experiment. Assuming the die is fair, the probability of it falling on 1, 2, 3, 4, 5 or 6 is 1/6 (evenly split). If we are given partial information about the final result e.g. The die falls on an even number (i.e either 2, 4 or 6), the conditional probabilities for all 6 faces of the die change. The probability of obtaining a 1, 3 or 5 will go down to 0, while the probability of obtaining a 2, 3 or 6 will go up to 2/6 (or 1/3). These new probabilities are conditioned on the fact that our result is even, and therefore called conditional probabilities.